On some algebras of truncated Hankel and asymmetric truncated Hankel operators

TL;DR

This paper explores the algebraic properties and interrelations of asymmetric truncated Hankel and Toeplitz operators, including their products and special cases with symmetric inner functions.

Contribution

It provides new results on the product structure and algebraic relations of these generalized operators, extending previous work on truncated operators.

Findings

Derived basic results on operator products

Established connections between asymmetric truncated Hankel and Toeplitz operators

Discussed algebraic properties under symmetric inner functions

Abstract

In the last decade, a large amount of research has been concentrated on the operators living on the model space. Asymmetric truncated Toeplitz operators and asymmetric truncated Hankel operators are the natural generalization of truncated Toeplitz operators and truncated Hankel operators respectively. In this paper, we obtained the basic results concerning the product of these operators and in terms of product their connection with each other. In addition, when the inner function has a certain symmetric property, some algebraic properties of truncated Hankel operators are also discussed.